Details

Time bar (total: 40.1s)

sample646.0ms

Algorithm
intervals
Results
431.0ms152×body1280valid
89.0ms70×body640valid
21.0ms25×body320valid
5.0ms9×body160valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01719
12819
23619
done3619

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.1b
(cos (- lambda1 lambda2))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 55
Calls
4 calls:
26.0ms
(* (sin phi1) (sin phi2))
9.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
15.0ms
(cos (- lambda1 lambda2))

series221.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin phi1) (sin phi2))
75.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
22.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
57.0ms
(cos (- lambda1 lambda2))

simplify7.1s

Counts
67 → 67
Iterations

Useful iterations: 2 (3.7s)

IterNodesCost
01111035
13451027
23804887
done5000887

prune499.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 64
Calls
4 calls:
21.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(* (sin phi1) (sin phi2))
7.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin lambda1) (sin lambda2))
83.0ms
(* (sin phi1) (sin phi2))
109.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
26.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify3.3s

Counts
76 → 76
Iterations

Useful iterations: 2 (938.0ms)

IterNodesCost
01331410
14771401
220821173
done50001173

prune669.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 4.2b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.6b
(log (exp (* (sin lambda1) (sin lambda2))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
5×add-log-exp
3×log-prod log-pow
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin exp-prod exp-to-pow rem-log-exp sin-mult
Counts
4 → 59
Calls
4 calls:
18.0ms
(* (sin phi1) (sin phi2))
7.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
5.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

series335.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (sin phi1) (sin phi2))
125.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
21.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
99.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

simplify2.3s

Counts
71 → 71
Iterations

Useful iterations: 2 (795.0ms)

IterNodesCost
01201473
13981364
220021146
done50001146

prune731.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (sin lambda1) (sin lambda2)) 3)
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
1.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
27.7b
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×pow1 add-exp-log add-cbrt-cube
8×cbrt-prod add-cube-cbrt *-un-lft-identity
4×add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod sin-mult rem-cube-cbrt sqr-pow
1×acos-asin pow-to-exp cbrt-div pow1/3 *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 67
Calls
4 calls:
18.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
15.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
3.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
5.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series326.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
108.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
26.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
99.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify1.6s

Counts
79 → 79
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01341690
16391464
done50011254

prune633.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 4.2b

regimes1.7s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02529
13329
done3329

end0.0ms

sample19.4s

Algorithm
intervals
Results
13.5s4768×body1280valid
4.3s2136×body640valid
543.0ms682×body320valid
137.0ms266×body160valid
68.0ms13×body2560valid
36.0ms136×body80valid